Is k-fold cross-validation more effective than splitting the dataset into training and test datasets to prevent overfitting?
K-fold cross-validation is probably preferred in terms of completeness and generalization: you ensure that the system has seen the complete dataset for training. However, in deep learning this is often not feasible due to time and power constraints. They can both be used, and there is not one better than the other. It really depends on the specific case, the size of the dataset and the time and hardware available. Note that overfitting can be (partially) remedied by things such as dropout.

To be fair: it is fine to have a discussion about this with your colleagues, but as so often there is no one correct answer. If you really want proof, you can test it out and compare them. But performance-wise (i.e. the model's predictive power), the difference will be small.